SCIENTIFIC PROGRAMS AND ACTIVITIES

November 27, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Focus Program on Commodities, Energy and Environmental Finance

August 14-16, 2013 (Wed-Fri)
Workshop on Electricity, Energy and Commodities Risk Management

Organizing Committee:
René Aïd, Matt Davison, Ivar Ekeland, Mike Ludkovski

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OVERVIEW

The workshop will address the recent developments in the mathematics and the practical management of risk emanating from recent trends in the electricity and energy markets, as well as financial tools to climate change mitigation and risk transfer. Many problems arising from the analysis of commodities and energy markets, demand the development of new mathematical tools. Some of the ongoing issues include incorporation of renewable energy production into the conventional power grid, complex correlations in electricity prices due to the multiple fuels used and impact of carbon allowances or taxes on electricity markets. These lead to challenges at the intersection of stochastic control, stochastic analysis, as well as computational methods. A goal of the workshop will be to foster interactions between academia and industry.

Preliminary Schedule

Wednesday, August 14
9:00-9:15
Opening Remarks
9:15-10:00
Olivier Feron, EDF (slides)
Commodity price modeling in EDF. Calibration and parameter estimation
10:00-10:45
Luciano Campi, University Paris 13 (slides)
Utility indifference valuation for non-smooth payoffs with an application to power derivatives
10:45-11:15
Coffee Break
11:15-12:00
Warren Powell, Princeton University
SMART-ISO: A Stochastic, Multiscale Model of the PJM Energy Markets
For slides, and more info: http://www.castlelab.princeton.edu/presentations.htm
12:00-1:45
Lunch Break
1:45-2:30
Almut Veraart, Imperial College London (slides)
Modelling electricity futures by ambit fields
2:30-3:15
Michel Denault, HEC-Montreal (slides)
An Approximate Dynamic Programming, Simulations and Regressions Approach to Value and Control a Hydropower System
3:15-3:45
Coffee Break
3:45-4:15
Imen Ben Tahar, University Paris Dauphine (slides)
Technological transition to electric mobility
4:15-4:45
Michael Kustermann, University Duisburg-Essen (slides)
A Structural Model for Interconnected Electricity Markets
5:15-6:15
Panel Discussion: "Environmental Finance and Commodities Markets: Opportunities and Challenges for Mathematicians"
Panelists:
René Aïd
, EDF
Rene Carmona, Princeton
Matt Davison, U Western Ontario
Ron Dembo, Zerofootprint
Thursday, August 15
9:15-10:00
Rudiger Kiesel, Universität Duisburg-Essen (slides)
Model Risk for Energy Markets
10:00-10:45
Fernando Auibe, Pontical Catholic University of Rio de Janeiro (slides)
The effects of shale gas on risk premium and volatility in the US gas prices
10:45-11:15
Coffee Break
11:15-12:00
Alejandro Jofré, Universidad Chile Santiago
Optimal pricing-regulations for a wholesale electricity market
12:00-1:45
Lunch Break
1:45-2:30
Michael Coulon, Princeton University (slides)
A model for Solar Renewable Energy Certificates: shining some light on price dynamics and optimal market design
2:30-3:15
Walid Mnif, University of Western Ontario (slides)
EU ETS Futures Spread Analysis and Recommendations for Effective Trading and Market Design
3:15-3:45
Coffee Break
3:45-5:15
Hans Tuenter (tutorial), Ontario Power Generation
The Modeling of Wind Energy

Friday, August 16
9:15-10:00
Eugenio Bobenrieth, Pontificia Universidad Católica de Chile (slides)
Stocks-to-use Ratios and Prices as Indicators of Vulnerability to Spikes in Global Cereal Markets
10:00-10:45
Delphine Lautier, Université Paris Dauphine
A simple equilibrium model for commodity markets
10:45-11:15
Coffee Break
11:15-12:00
Pascal Heider, E.ON Global Commodities SE (slides)
Co-integrated Commodities, Proxy-Hedges and Structured Cash-Flows
12:00-2:00
Lunch Break
2:00-2:45
Jorge Zubelli, IMPA
Investment Decisions under Uncertainty, Real Options and Commodity Models
2:45-3:20
Coffee Break
3:20-3:50
Marcus Eriksson, University of Oslo, Norway
Energy derivatives with volume control
3:50-4:20
Christian Maxwell, University of Western Ontario (slides)
Using Real Option Analysis to Quantify Ethanol Policy Impact on the Firm's Entry Into and Optimal Operation of Corn Ethanol Facilities
Speaker Talk Title and Abstract
Fernando Aiube
Pontical Catholic University of Rio de Janeiro

The effects of shale gas on risk premium and volatility in the US gas prices

The change in the US natural gas market was enormous in recent years. The expectations on the abundance of shale gas supply pushed gas prices lower than US$ 4/MM Btu. Governmental projections for 2018 maintain this lower price scenario. The successful technologies of horizontal drilling and hydraulic fracturing simultaneously enabled the increase of the recoverable volumes to 482 trillion cubic feet (US EIA 2012 report). Although shale gas is a new promising source of unconventional energy, investors are dealing with uncertainties regarding their investment plans.
We investigate how the behavior of the risk premium and volatility have been affected by the new era of low prices. Di erently from the traditional empirical researches on risk premium, we use the parametric two-factor model of Schwartz and Smith (2000) to evaluate the implied-risk premium term-structure from futures prices traded on NYMEX. We also investigate the structural breaks on the gas prices time series and adjust volatility long memory GARCH-class models.

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Imen Ben Tahar
University Paris Dauphine

Technological transition to electric mobility

The context is that of a secular competition between the electrical vehicle (EV) and the fossile-fuel-powered vehicle (FV). In the early years of the automotive industry none of these technologies dominated, but rapidly, the fossile-fuel-powered internal combustion engine has established itself as the dominant technology option. There have been episodes of renewed interest in electric mobility : in the 70’s, due to oil crisis, then in the 90’s mainly motivated by the negative effects of air pollution. These attempts failed to provide electric mobility a sufficient momentum in order to escape the technological lock-in. Now, times are changing : recent socio-technical developments have the potential to trigger the emergence of a viable trajectory for electric mobility. Still, there is a need for convenient policies in order to allow these new developments to overcome the factors which work against.

We propose a model for the evolution of the (EV) market and aim to quantify the impact of subsidizing purchases of (EVs). Here, the aim of the regulator when subsidizing purchases of (EVs) is to maximize the social benefit identified with the realized fuel economy. This is joint work with Rene Aid.
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Eugenio Bobenrieth
Pontificia Universidad Católica de Chile

Stocks-to-use Ratios and Prices as Indicators of Vulnerability to Spikes in Global Cereal Markets

We identify critical stocks-to-use ratios (SURs) for major grains and for an index of total calories from these grains. The latter appears to be a promising indicator of vulnerability to large price spikes when the current price shows no cause for concern. More generally, our results suggest that stocks data, though no doubt unreliable, can be valuable complements to price data as indicators of vulnerability to shortages and price spikes.

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Luciano Campi
University Paris 13

Utility indifference valuation for non-smooth payoffs with an application to power derivatives

We consider the problem of exponential utility indifference valuation under the simplified framework where traded and nontraded assets are uncorrelated but where the claim to be priced possibly depends on both. Traded asset prices follows a multivariate Black and Scholes model, while non traded asset prices evolve as generalized Ornstein-Uhlenbeck processes. We provide a BSDE characterization of the utility indifference price for a large class of non-smooth payoffs depending simultaneously on both classes of assets. The Markovian setting and the Gaussian property of non traded assets allow us to characterize the utility indifference price for possibly discontinuous European payoffs as the unique viscosity solution of a suitable PDE and the optimal hedging strategy as essentially the delta hedging strategy corresponding to such a price. Moreover, we obtain asymptotic expansions for prices and hedging strategies when the risk aversion parameter is small. Finally, our results are applied to pricing and hedging power derivatives in various structural models for energy markets. This is a joint work with G. Benedetti.

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Michael Coulon
Princeton University

A model for Solar Renewable Energy Certificates: shining some light on price dynamics and optimal market design

Markets for solar renewable energy certificates (SRECs) are a new tool for energy and environmental policy, gaining in prominence in many regions nowadays, and nowhere more so than in the American state of New Jersey on which we base our study. However, SREC market prices have proven to be extremely volatile in the past few years, causing high risk to market participants and less investment in solar power generation. Such concerns necessitate the development of realistic and tractable SREC price models, with the flexibility to adapt and calibrate to rapidly changing markets. We propose an original stochastic modeling framework to fill this role, drawing on established ideas from carbon allowance price modeling, and including a feedback mechanism for solar generation response to market prices. We also analyze and propose various alternative rules capable of improving market performance, thus providing some insight into the crucial role played by regulatory policy and market design.

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Michel Denault
HEC-Montreal

An Approximate Dynamic Programming, Simulations and Regressions Approach to Value and Control a Hydropower System

We investigate the control of a stochastic system, in the presence of both an exogenous (control-independent) stochastic state variable and an endogenous (control-dependent) state variable. Our solution approach relies on simulations and regressions for both types of variables, as the endogenous variable is gradually integrated into the simulation paths. Unlike most approaches found in the literature, no discretization of the endogenous variable is required. The algorithm is applied to optimize the storage decisions for a hydropower system in half-day increments, over long periods, and with multiscale seasonalities.

This is joint work with Jean-Guy Simonato and Lars Stentoft.
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Marcus Eriksson
University of Oslo, Norway

Energy derivatives with volume control

Electricity producers face a price risk as well as a volume risk. In this talk we capture a way to hedge for the volume risk feature in power market derivatives. We formulate the value of such a derivative, e.g. a flexible load contract, in terms of a stochastic control problem. Mathematically, we define a value function for the contract and put constraints on the control variable Z, representing a volume, such that the total volume at maturity satisfy some predefined conditions. In particular we consider a minimal (m) and a maximal (M) volume constraint. i.e. Z(T) is in the interval [m,M] at maturity T. By Bellman's principle we show that the optimal value is obtained as a solution to an Hamilton-Jacobi-Bellman equation via a verification theorem. We also show some properties of the value function. Furthermore, we investigate the situation when we relax the minimal constraint, but instead consider a penalty if Z(T)<m.

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Olivier Feron
EDF

Commodity price modeling in EDF. Calibration and parameter estimation

This presentation focuses on commodity price modeling used in EDF for risk management purposes and the necessary step of model parameter determination. In particular, the objective of this presentation is firstly to expose the constraints of modeling we must face (exposition, available hedging products, multiple using of a single model…) and give a description of the currently used model in EDF for risk management, with the different existing methods of calibration. In a second step we propose to describe a study on forward price reconstruction from the structural model described in [1]. In this context we give first results on forward reconstruction with the introduction of a “model uncertainty”. We also present some results on the calibration process from observed forward prices, allowing studying how the market is using some “hidden” information on the relationship between commodities.

[1] R. Aïd, L. Campi and N. Langrené, "A structural risk-neutral model for pricing and hedging power derivatives ", hal-00525800, to appear in Mathematical Finance
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Pascal Heider
E.ON Global Commodities SE
Co-integrated Commodities, Proxy-Hedges and Structured Cash-Flows

Typically, commodities are tied together by fundamental relationships, e.g. fossil fuels are burnt to produce power, crude oil is refined to produce petroleum products, gas prices can be linked to oil indices, and many more … . We show that the concept of co-integration yields interesting correlation relationships between commodities. In this talk we discuss explicit formulas and study the impact on valuation and risk management of structured cash flows and the definition of proxy hedges. This is a joint work with Rainer Döttling.

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Alejandro Jofré
Universidad de Chile

Optimal pricing-regulations for a wholesale electricity market

We introduce a wholesale electricity market model with generators interacting strategically and including externalities such as transmission losses on a general network. Previous works by the author show how mechanisms based on Lagrange multipliers of a centralized cost minimization program allow the producers to charge significantly more than marginal price originating an important regulatory problem. In this presentation we consider an incomplete information setting in which the cost structure of a producer is partially unknown. We derive an optimal regulation mechanism and compare its performance to the "price equal to Lagrange multiplier" rule.

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Rüdiger Kiesel
Universität Duisburg-Essen
Model Risk for Energy Markets

Recently, model risk, in particular parameter uncertainty, has been addressed for financial derivatives. During this talk we will review these concepts and apply the methods to energy markets. In particular, we will discuss parameter uncertainty for spread options and implications for fossil power plant valuation. To capture model risk we use a methodology recently established in a series of papers by Bannör and Scherer. As gas-fired power plants are seen as flexible and low-carbon sources of electricity which are important building blocks in terms of the switch to a low-carbon energy generation, we consider the model risk in this asset class in detail. Our findings reveal that spike risk is by far the most important source of model risk.
(Based on joint work with Karl Bannör, Anna Nazarova and Matthias Scherer).

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Michael Kustermann
University Duisburg-Essen

A Structural Model for Interconnected Electricity Markets

Structural or hybrid models have become very popular to model electricity spot prices due to the fact that risk factors driving supply and demand are better understood and easier observable than in most other markets. However, one very important risk factor - import and export - could not be modeled endogenously in such a model. We propose a multi-market extension of the class of Structural models which is able to capture the subtle interplay between separated but interconnected electricity markets.

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Delphine Lautier
Université Paris Dauphine

A simple equilibrium model for commodity markets
Authors : Ivar Ekeland, Delphine Lautier, Bertrand Villeneuve

We propose a simple equilibrium model, where the physical and the derivative markets of the commodity interact.There are three types of agents: industrial processors, inventory holders and speculators. Only the two first of them operate in the physical market. All of them, however, may initiate a position in the paper market, for hedging and/or speculation purposes. We give the necessary and sufficient conditions on the fundamentals of this economy for a rational expectations equilibrium to exist and we show that it is unique. This is
the first contribution of the paper. Our model exhibits a surprising variety of behaviours at equilibrium, and our second contribution is that the paper offers a unique generalized framework for the analysis of price relationships. The model indeed allows for the generalization of hedging pressure theory, and it shows how this theory is connected to the storage theory. Meanwhile, it allows to study simultaneously the two main economic functions of derivative markets: hedging and price discovery. In its third contribution, through the distinction between the utility of speculation and that of hedging, the model illustrates the interest of a derivatives market in terms of the welfare of the agents.

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Christian Maxwell
University of Western Ontario
Using Real Option Analysis to Quantify Ethanol Policy Impact on the Firm's Entry Into and Optimal Operation of Corn Ethanol Facilities

Ethanol crush spreads are used to model the value of a facility which produces ethanol from corn. A real options analysis is used to investigate the effects of energy policy on management's decision to operate the facility through optimal switching and the firm's decision to enter into the project. We perform the analysis using PDE techniques by means of a layered stochastic optimal control problem via optimal exercise into a switching problem. We present evidence of increased correlation between corn and ethanol prices, perhaps as a result of government policy which has induced more players to enter into the market. This talk investigates the subsequent negative impact on valuations. Further, this talk illustrates the impact of policy uncertainty via a stochastic process which models the possibility of a future abrupt change in government policy on a firm's decision to enter the business.

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Walid Mnif
University of Western Ontario

EU ETS Futures Spread Analysis and Recommendations for Effective Trading and Market Design

The European Union Emission Trading Scheme (EU ETS) is the leading cap-and-trade market that has been implemented with the aim of decreasing global greenhouse gas emissions over both the short and long time horizons. Based on the EU ETS experience, we analyze the observed spread between futures contracts with different maturities. Discrete and continuous time models are proposed. We suggest recommendations for effective trading and market design. Economic conclusions are drawn.

This is a joint work with Matt Davison (Western University).

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Warren Powell
Princeton University

SMART-ISO: A Stochastic, Multiscale Model of the PJM Energy Markets

We will describe the development of a detailed stochastic, dynamic model of the PJM energy markets which is being designed with the goal of performing a wide range of simulations to test the effect of high penetrations of renewables. SMART-ISO includes a full model of the PJM power grid, a robust day-ahead model for stochastic unit commitment, hour-ahead modeling for planning natural gas simulation, economic dispatch solved at five minute increments, and real-time solution of an AC power flow model. The fine-grained time scales are designed for accurate modeling of ramp rates of natural gas units and variations in renewables. A central feature of the model is the careful handling of uncertainty. A stochastic model of wind has been developed for both day-ahead and hour-ahead forecasts. The day-ahead model uses a quantile-optimization algorithm with feedback learning to produce robust plans for steam generation, while the hour-ahead and economic dispatch models use approximate dynamic programming to plan energy storage while meeting real-time demands. We will report on recent work calibrating LMPs, and current research evaluating the impact of the integration of off-shore wind. For more on SMART-ISO, see http://energysystems.princeton.edu/smartiso.htm. |
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Hans JH Tuenter
Ontario Power Generation

The Modeling of Wind Energy

This talk will give an overview of the different elements that one needs in order to produce realistic wind forecasts that can be used in the energy sector. We will focus on short-term, operational time-frame forecasts and discuss the applications of (and learning experiences with) our in-house developed forecasting system.

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Almut Veraart
Imperial College London
Modelling electricity futures by ambit fields

This paper proposes a new modelling framework for electricity futures based on so-called ambit fields. The new model can capture many of the stylised facts observed in electricity futures and is highly analytically tractable. We discuss martingale conditions, option pricing and change of measure within the new model class. Also, we study the corresponding model for the spot price, which is implied by the new futures model and show that, under certain regularity conditions, the implied spot price can be represented in law as a volatility modulated Volterra process. This is joint work with Ole E. Barndorff-Nielsen (Aarhus University) and Fred Espen Benth (University of Oslo).
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Jorge Zubelli
IMPA

Investment Decisions under Uncertainty, Real Options and Commodity Models

Industrial strategic decisions have evolved tremendously in the last decades towards a higher degree of quantitative analysis. Such decisions require taking into account a large number of uncertain variables and volatile scenarios, much like financial market investments. Furthermore, they can be evaluated by comparing to portfolios of investments in financial assets such as in stocks, derivatives and commodity futures. This revolution led to the development of a new field of managerial science known as Real Options.

The use of Real Option techniques incorporates also the value of flexibility and gives a broader view of many business decisions that brings in techniques from quantitative finance and risk management. Such techniques are now part of the decision making process of many corporations and require a substantial amount of mathematical background. Yet, there has been substantial debate concerning the use of risk neutral pricing and hedging arguments to the context of project evaluation. We discuss some alternatives to risk neutral pricing that could be suitable to evaluation of projects in a realistic context with special attention to projects dependent on commodities and non-hedgeable uncertainties.
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